Question

Hi! Got stuck after first step.
Write as an exact log:
2^x = 3^(x-1)
1. 2^x = 3^x * (1/3)

Where should I go from here? Thanks so much!

Answer 1

Noooo, let's back that step up.
Take natural log as first step.

Answer 2

\[\large\rm \ln(2^x)=\ln(3^{(x-1)})\]

Answer 3

Apply this log rule to each side: \(\large\rm \log(a^b)=b\cdot\log(a)\)

Answer 4

\[\large\rm x\ln(2)=(x-1)\ln(3)\]Then solve for x.